How do I remove these spaces?

[kobra]

Of course it is broken when you remove the CSS. The divs that wrap the site have no definitions without the CSS.

Not all 6 of the css files that you are loading just the non zen style.css file. Try it! Rename it to style.txt and load your site. See that your css is also messing with the layout and why I initially posted that you should merge these files.
But you adamantly contend that your css is not controlling the site layout.